Table 1 f(α) and g(α) kinetic functions corresponding to the most widely employed kinetic models
Mechanism | Symbol | f(α) | f(α) |
|---|---|---|---|
Phase boundary controlled reaction (contracting area) | R2 | 2(1 − α)1/2 | 2[1 − (1 − α)1/2] |
Phase boundary controlled reaction (contracting volume) | R3 | 3(1 − α)2/3 | 3[1 − (1 − α)2/3] |
First order kinetics or Random nucleation followed by an instantaneous growth of nuclei. (Avrami-Erofeev eqn. n =1) | F1 | (1 − α) | − ln(1 − α) |
Random nucleation and growth of nuclei through different nucleation and nucleus growth models. (Avrami-Erofeev eqn ≠1.) | An | n(1 − α) [−ln(1 − α)]1 − 1/n | [−ln(1 − α)]1 − 1/n |
Two-dimensional diffusion | D2 | 1/[−ln(1 − α)] | (1 − α)ln(1 − α) + α |
Three-dimensional diffusion (Jander equation) | D3 |
| [1 − (1 − α)1/3]2 |
Three-dimensional diffusion (Ginstling-Brounshtein equation) | D4 |
| (1 − 2α/3) − (1 − α)2/3 |
Random Scission L=2 [10] | L2 | 2(α1/2 − α) | − 2 ln(α1/2 − 1) |
Random Scission L>2 [10] | Ln | No symbolic solution | No symbolic solution |